Beat the egg whites with an electric mixer until stiff. Line a large baking sheet with waxed paper. Put the sugar, corn syrup and water in a heavy medium-size saucepan over medium-high heat. Stir to dissolve the sugar, then bring to a boil and cook until the temperature reaches 260 degrees on a candy thermometer. Remove from heat. Pour in a thin, steady stream into the beaten egg whites and beat with an electric mixer on high for about 3 minutes, scraping down the sides of the bowl to mix well.
Add the vanilla and continue beating on high until the candy starts to lose its gloss (about 5 to 6 minutes). When the beaters are lifted from the bowl, the mixture should fall in a ribbon that mounds on itself.
If the mixture flattens out, beat again for 1 minute longer. If the mixture is too thick to drop, beat in a few drops of hot water until the candy is softer in consistency. Add the chopped pecans and stir to mix. Quickly drop the candy mixture by tablespoonfuls onto the prepared baking sheet. Allow fudge to set up, then serve.